For most of the East-Bay-to-South-Bay segment (from Santa Clara to around Fremont), there is only one track. That's not unusual in freight rail, but what's missing here are passing points: Long sidings where one train can get out of the way of a passing train.
You can see the route around the bay here: https://www.youtube.com/watch?v=yoyZC4LvKoI
Also, Union Pacific owns the tracks used by the Capitol Corridor, so priority becomes a question: Yes, passenger rail is supposed to be higher priority, but UP can (and does) charge Amtrak for using the rails. Railroads can (and have) demand that passenger railroads pay to build/upgrade infrastructure as a condition for running more passenger trains.
So yes, it would be doable, but it would be _expensive_.
But its irrelevant till you double track Alviso.